Wave-number–frequency spectrum for turbulence from a random sweeping hypothesis with mean flow

We derive the energy spectrum in wave-number-frequency space for turbulent flows based on Kraichnan's idealized random sweeping hypothesis with additional mean flow, which yields the instantaneous energy spectrum multiplied by a Gaussian frequency distribution. The model spectrum has two adjustable parameters, the mean flow velocity and the sweeping velocity, and has the property that the power-law index of the wave-number spectrum translates to the frequency spectrum, invariant for arbitrary choices of the mean velocity and sweeping velocity. The model spectrum incorporates both Taylor's frozen-in flow approximation and the random sweeping approximation in a natural way and can be used to distinguish between these two effects when applied to real time-resolved multipoint turbulence data. Evaluated in real space, its properties with respect to space-time velocity correlations are discussed, and a comparison to the recently introduced elliptic model is drawn.